Block #272,294

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 4:29:44 AM · Difficulty 9.9526 · 6,536,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e63897b4299d6b10e4b73ad24c206733d1ace7a897f11fecb107481be637c5d3

View on Chainz ↗

Height

#272,294

Difficulty

9.952574

Transactions

Size

1.08 KB

Version

Bits

09f3dbec

Nonce

85,125

Timestamp

11/25/2013, 4:29:44 AM

Confirmations

6,536,101

Mined by

⛏️ P2SHAYDrV3Chn9pDpvzSLArAoNHaYybApZ4S5M

Merkle Root

9bf1220f53bda9bd930642e222c4a3c13b9418a92bf21b8bffd433bc30b30865

Transactions (4)

Coinbase65f0c63cce28d7…65bc5e859ac03b

1 in → 1 out10.1143 XPM109 B

AYDrV3Ch…bApZ4S5M

f1a0062be414e7…883b3175d1f7aa

1 in → 1 out999.9900 XPM192 B

AbuEpxmh…Ru6xLtB1

1e69f4e14bec4f…f6ad488a24af6f

3 in → 1 out3.1900 XPM487 B

AZLL3Fjt…ez6JMifD

daab909f20b604…701b3fc9c4424c

1 in → 2 out2.9986 XPM226 B

ASrjzNVY…jvPSQnAH AaVFHFSq…bCnX1Bpw

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.

9.701 × 10⁹⁵(96-digit number)

97015835303513066405…42814888985757240319

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

9.701 × 10⁹⁵(96-digit number)

97015835303513066405…42814888985757240319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.701 × 10⁹⁵(96-digit number)

97015835303513066405…42814888985757240321

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

1.940 × 10⁹⁶(97-digit number)

19403167060702613281…85629777971514480639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.940 × 10⁹⁶(97-digit number)

19403167060702613281…85629777971514480641

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

3.880 × 10⁹⁶(97-digit number)

38806334121405226562…71259555943028961279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.880 × 10⁹⁶(97-digit number)

38806334121405226562…71259555943028961281

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

7.761 × 10⁹⁶(97-digit number)

77612668242810453124…42519111886057922559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.761 × 10⁹⁶(97-digit number)

77612668242810453124…42519111886057922561

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

1.552 × 10⁹⁷(98-digit number)

15522533648562090624…85038223772115845119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.552 × 10⁹⁷(98-digit number)

15522533648562090624…85038223772115845121

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #272,294

Cookie Preferences