Block #254,519

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 6:31:47 PM · Difficulty 9.9732 · 6,548,111 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bcb313736d475ba8dbb23d28e8a1240a2c292d041cf8ad5a9c9ad6415c4fc81a

View on Chainz ↗

Height

#254,519

Difficulty

9.973234

Transactions

Size

2.81 KB

Version

Bits

09f925de

Nonce

65,739

Timestamp

11/10/2013, 6:31:47 PM

Confirmations

6,548,111

Mined by

⛏️ 7aRVAZo5FC5zoaKVWDnk5yty4CrSh2Gkux5Vms

Merkle Root

d9cfd2685ade80276d4baf0b9e7491d70d3e89f1e03da2bd9b44f95561aca6de

Transactions (4)

Coinbase568030d1694643…02eb82db5b5dfd

1 in → 58 out10.0100 XPM1.99 KB

AZo5FC5z…Gkux5Vms AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5 AYckRkCF…TgDe5VSp

c9a13138cb255b…305f34f1b057fa

2 in → 2 out200.0000 XPM373 B

AJWinvX2…mqNxXU9e ATJi3RtC…sSxGmpuT

6c4543cb6fbc90…c16be169dcc959

1 in → 1 out10.0400 XPM158 B

AZbnPqqW…8cDz5Rfd

8f8a7d804a0ea7…f709f218133fcb

1 in → 2 out3.0509 XPM226 B

AHuPK4ck…rnwbhTG3 AbjLQB3Y…SXLCXwVY

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.

6.921 × 10⁹¹(92-digit number)

69218029547429168450…04455715702725517199

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

6.921 × 10⁹¹(92-digit number)

69218029547429168450…04455715702725517199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.921 × 10⁹¹(92-digit number)

69218029547429168450…04455715702725517201

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

1.384 × 10⁹²(93-digit number)

13843605909485833690…08911431405451034399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.384 × 10⁹²(93-digit number)

13843605909485833690…08911431405451034401

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

2.768 × 10⁹²(93-digit number)

27687211818971667380…17822862810902068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.768 × 10⁹²(93-digit number)

27687211818971667380…17822862810902068801

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

5.537 × 10⁹²(93-digit number)

55374423637943334760…35645725621804137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.537 × 10⁹²(93-digit number)

55374423637943334760…35645725621804137601

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

1.107 × 10⁹³(94-digit number)

11074884727588666952…71291451243608275199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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