Block #155,232

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 4:51:22 AM · Difficulty 9.8655 · 6,650,615 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e542a4de0cee61c4cd2a55d8fd5680b0e79ee69e666c3d4f2164d810efc929c

View on Chainz ↗

Height

#155,232

Difficulty

9.865468

Transactions

Size

5.98 KB

Version

Bits

09dd8f52

Nonce

35,816

Timestamp

9/8/2013, 4:51:22 AM

Confirmations

6,650,615

Mined by

⛏️ P2SHAN4pfsaVXqP3cYRnBKFGRNbyU1VbXj1QVx

Merkle Root

6bcf30322c3d3db07c2b152764548b7335b7766ec4f1ec1424df242943f69f04

Transactions (4)

Coinbase89327ae4ce93d7…cc780cabccbc81

1 in → 1 out10.3400 XPM109 B

AN4pfsaV…VbXj1QVx

7096f0bcf7f105…1d778eb81f8d69

45 in → 1 out463.3800 XPM5.06 KB

AaZTHvEh…QXHS2iBB

8f9dad2df9f3f2…e2378b03e84a19

1 in → 2 out6.0672 XPM227 B

AVYA5FSq…eeZm8KGY AYPCrmfr…uTAfBZLb

ef13c55e3d8bd5…9f8a4133a6f18d

3 in → 2 out10.1278 XPM522 B

AMqJPEMv…gbeSGzME AHyHEeYQ…XuELsExj

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.

1.747 × 10⁸⁸(89-digit number)

17470865758711776441…74350437959056987529

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

1.747 × 10⁸⁸(89-digit number)

17470865758711776441…74350437959056987529

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.747 × 10⁸⁸(89-digit number)

17470865758711776441…74350437959056987531

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

3.494 × 10⁸⁸(89-digit number)

34941731517423552883…48700875918113975059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.494 × 10⁸⁸(89-digit number)

34941731517423552883…48700875918113975061

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

6.988 × 10⁸⁸(89-digit number)

69883463034847105766…97401751836227950119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.988 × 10⁸⁸(89-digit number)

69883463034847105766…97401751836227950121

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

1.397 × 10⁸⁹(90-digit number)

13976692606969421153…94803503672455900239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.397 × 10⁸⁹(90-digit number)

13976692606969421153…94803503672455900241

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

2.795 × 10⁸⁹(90-digit number)

27953385213938842306…89607007344911800479

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