Block #2,655,008

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/9/2018, 7:56:49 PM · Difficulty 11.7114 · 4,189,073 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b65b78e0ac95d73bf7db3c94ff15e6e0e25c909cc671e5b78c4ad97aff6e90b5

View on Chainz ↗

Height

#2,655,008

Difficulty

11.711391

Transactions

Size

2.28 KB

Version

Bits

0bb61db4

Nonce

9,960,543

Timestamp

5/9/2018, 7:56:49 PM

Confirmations

4,189,073

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

158f8888514c05dadcf620615ec94df22c51ffe7cbbbee415f9148cc8a67dc49

Transactions (5)

Coinbased6cfd61d397c92…e5271d92614a54

1 in → 1 out7.3300 XPM110 B

Adqah8zh…1WwoHJ9t

2e3aeab645ef99…4d2ea0d5f2fb02

2 in → 2 out14.4300 XPM307 B

AW3QZZmg…j2rGjUkp AVdZbUGK…3mZroNbg

b96df011f0a2d7…3bfcd98198f36e

2 in → 2 out11.6500 XPM341 B

AH8UAN4u…zxwiJkLN AL61HLzk…GALLZgJu

e85a79c8c44cbe…29f73c25bd1818

8 in → 2 out3.0673 XPM1.24 KB

AGfqUaUj…eJKqdATL AWp4iAg7…FUBLEm8x

2154e2ff7a9dca…43142efe4a0048

1 in → 2 out0.1639 XPM226 B

AVUwNiAp…ngwN5wUc AN7b55gz…YroqkbjU

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.

3.838 × 10⁹⁴(95-digit number)

38386684359762837186…51775120360868012799

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

3.838 × 10⁹⁴(95-digit number)

38386684359762837186…51775120360868012799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.838 × 10⁹⁴(95-digit number)

38386684359762837186…51775120360868012801

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

7.677 × 10⁹⁴(95-digit number)

76773368719525674373…03550240721736025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.677 × 10⁹⁴(95-digit number)

76773368719525674373…03550240721736025601

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

1.535 × 10⁹⁵(96-digit number)

15354673743905134874…07100481443472051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.535 × 10⁹⁵(96-digit number)

15354673743905134874…07100481443472051201

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

3.070 × 10⁹⁵(96-digit number)

30709347487810269749…14200962886944102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.070 × 10⁹⁵(96-digit number)

30709347487810269749…14200962886944102401

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

6.141 × 10⁹⁵(96-digit number)

61418694975620539498…28401925773888204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.141 × 10⁹⁵(96-digit number)

61418694975620539498…28401925773888204801

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

1.228 × 10⁹⁶(97-digit number)

12283738995124107899…56803851547776409599

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 #2,655,008

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