Block #2,634,497

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 4/28/2018, 10:16:28 PM · Difficulty 11.2487 · 4,202,405 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

5cd9b8650b593adca255f47cf53fe297079c9b0974a9e0f50002ee1293416d95

View on Chainz ↗

Height

#2,634,497

Difficulty

11.248711

Transactions

Size

1.97 KB

Version

Bits

0b3fab83

Nonce

1,254,542,338

Timestamp

4/28/2018, 10:16:28 PM

Confirmations

4,202,405

Mined by

⛏️ P2SHAK9JectkY74H13QPsXWvL8nxGaShR1HiVi

Merkle Root

06c220d2ceb56f20c1448bf3524d3bb8f91962d0e51760f7f9c86b6dc0497fa6

Transactions (5)

Coinbase0b4fd1e1ce1731…b929da148c2da2

1 in → 1 out7.9300 XPM110 B

AK9Jectk…ShR1HiVi

9dd3aec54063f2…29a3eea23a6fbb

7 in → 2 out55.9900 XPM874 B

ANWdJ2nc…BW7RisDk AejwZDkS…4jbENvV1

f8434821bab918…b1aa58d3378fdf

1 in → 2 out7.9800 XPM191 B

AdFCNshJ…ZyXgrX3S AdKhEL4Q…RQS9ZydR

fea5b401ac7c77…e53300cc90e10a

2 in → 2 out5.4820 XPM373 B

ATrGEXEY…wfqvhS3J AWp4iAg7…FUBLEm8x

c3c99ddd12dc6e…1501a65725da12

2 in → 2 out4.0220 XPM375 B

AYUY6QBZ…nstBEWCQ ARHVEyPW…ejzijD2W

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.275 × 10⁹⁹(100-digit number)

12752516630444879385…72147129551088844799

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.275 × 10⁹⁹(100-digit number)

12752516630444879385…72147129551088844799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10⁹⁹(100-digit number)

12752516630444879385…72147129551088844801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.550 × 10⁹⁹(100-digit number)

25505033260889758770…44294259102177689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.550 × 10⁹⁹(100-digit number)

25505033260889758770…44294259102177689601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

5.101 × 10⁹⁹(100-digit number)

51010066521779517540…88588518204355379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.101 × 10⁹⁹(100-digit number)

51010066521779517540…88588518204355379201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.020 × 10¹⁰⁰(101-digit number)

10202013304355903508…77177036408710758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10¹⁰⁰(101-digit number)

10202013304355903508…77177036408710758401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

2.040 × 10¹⁰⁰(101-digit number)

20404026608711807016…54354072817421516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.040 × 10¹⁰⁰(101-digit number)

20404026608711807016…54354072817421516801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.080 × 10¹⁰⁰(101-digit number)

40808053217423614032…08708145634843033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.080 × 10¹⁰⁰(101-digit number)

40808053217423614032…08708145634843033601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,634,497

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