Block #137,739

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 12:08:40 AM · Difficulty 9.8226 · 6,665,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bcae038870fe2bf0c951eeb24fe7facf959fbb8b8dd48ec414c6467d7666e8da

View on Chainz ↗

Height

#137,739

Difficulty

9.822556

Transactions

Size

1.11 KB

Version

Bits

09d29304

Nonce

239,502

Timestamp

8/28/2013, 12:08:40 AM

Confirmations

6,665,758

Mined by

⛏️ P2SHAUBma4S5uySZMrn3ZFMcGzLaC1FQrLorT7

Merkle Root

b374759ab1eda97ec2eba9c107c21ee5bb9a45c7673636d705effdec5c1d36fc

Transactions (4)

Coinbaseb2c2c10811de5e…5f6fb3d0aede34

1 in → 1 out10.3800 XPM109 B

AUBma4S5…FQrLorT7

fec3d436c5dbc1…1884de25388cda

3 in → 1 out15.2307 XPM486 B

AYdStrmQ…4GzmBTU9

d4900b1cc39091…3c7948df9ba4c2

1 in → 2 out10.3800 XPM225 B

AMnPktYu…TWWsrN9u AYCDGrAB…Ld4zi8J7

b4a86b757b88ba…1d5233cf491074

1 in → 2 out2.8719 XPM226 B

AKek8pkA…t2Hyb26f AVKfZvtY…sCa4NTcM

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.

9.624 × 10⁹³(94-digit number)

96246860781116334104…06671474643211402479

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

9.624 × 10⁹³(94-digit number)

96246860781116334104…06671474643211402479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.624 × 10⁹³(94-digit number)

96246860781116334104…06671474643211402481

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

1.924 × 10⁹⁴(95-digit number)

19249372156223266820…13342949286422804959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.924 × 10⁹⁴(95-digit number)

19249372156223266820…13342949286422804961

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

3.849 × 10⁹⁴(95-digit number)

38498744312446533641…26685898572845609919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.849 × 10⁹⁴(95-digit number)

38498744312446533641…26685898572845609921

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

7.699 × 10⁹⁴(95-digit number)

76997488624893067283…53371797145691219839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.699 × 10⁹⁴(95-digit number)

76997488624893067283…53371797145691219841

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

1.539 × 10⁹⁵(96-digit number)

15399497724978613456…06743594291382439679

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