Block #1,908,908

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/25/2016, 1:45:26 AM · Difficulty 10.7436 · 4,932,200 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5895309bb321529e8fbecf41ee62c95abe4f341e9ec6f755076a9fafeee0c98

View on Chainz ↗

Height

#1,908,908

Difficulty

10.743604

Transactions

Size

699 B

Version

Bits

0abe5cdb

Nonce

374,704,484

Timestamp

12/25/2016, 1:45:26 AM

Confirmations

4,932,200

Mined by

⛏️ P2SHAdQRm19BdS9TaNvDp4wVRn5ScMizzsMPbQ

Merkle Root

1d7c296be7d37edd6bfb61d4f0e4e0a325bdff70f04d1c8b7c77359580514004

Transactions (2)

Coinbase8894bac7489b19…c52ebba6f14c38

1 in → 1 out8.6600 XPM109 B

AdQRm19B…izzsMPbQ

9ef270ac2f42b4…92dec4d8a3c581

1 in → 10 out6.0753 XPM499 B

AHva16vh…vCv9VmMa AdRDwd5e…tRPzdTrr AS2nbS17…LqfxA5Xe AZ7awCVY…uoCoV8WY AWw8WFNW…gTmadNVV

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.

4.821 × 10⁹⁶(97-digit number)

48210900734897216277…76692678200234618879

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

4.821 × 10⁹⁶(97-digit number)

48210900734897216277…76692678200234618879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.821 × 10⁹⁶(97-digit number)

48210900734897216277…76692678200234618881

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

9.642 × 10⁹⁶(97-digit number)

96421801469794432555…53385356400469237759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.642 × 10⁹⁶(97-digit number)

96421801469794432555…53385356400469237761

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

1.928 × 10⁹⁷(98-digit number)

19284360293958886511…06770712800938475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.928 × 10⁹⁷(98-digit number)

19284360293958886511…06770712800938475521

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

3.856 × 10⁹⁷(98-digit number)

38568720587917773022…13541425601876951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.856 × 10⁹⁷(98-digit number)

38568720587917773022…13541425601876951041

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

7.713 × 10⁹⁷(98-digit number)

77137441175835546044…27082851203753902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.713 × 10⁹⁷(98-digit number)

77137441175835546044…27082851203753902081

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

1.542 × 10⁹⁸(99-digit number)

15427488235167109208…54165702407507804159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,908,908

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