Block #314,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 6:19:11 AM · Difficulty 10.0793 · 6,481,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56bd8c4cd39fe762025a22737120792560d9b7f4f8a91276afa2c06fb8be3b62

View on Chainz ↗

Height

#314,948

Difficulty

10.079285

Transactions

Size

1.77 KB

Version

Bits

0a144c05

Nonce

232,988

Timestamp

12/16/2013, 6:19:11 AM

Confirmations

6,481,067

Mined by

⛏️ DaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

7970b326994fff92a218b0604ff9c6f8d0ab232e8e96840cd7b2169cfd40739e

Transactions (4)

Coinbase22fd62348f877a…396fb822d06c59

1 in → 29 out9.8100 XPM1.02 KB

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz ARF6Rjqp…rnYCbZhi AGPBDvpY…HsUDJ9oq APeshfYV…3PKcKMKH

1f1e92bcd09f7a…8fb12d21eb2118

1 in → 2 out4.9061 XPM225 B

AMd8ihtX…LWpNWsLh AGWtVz76…kbdYi19h

28ddce2676568b…5cd0eb5ba84a90

1 in → 2 out4.8375 XPM225 B

AeWK6Zk2…L5BsDAtZ ARbtU6Bw…JhnjB6fy

0aa1c37d5c2aad…7b9cf9c11a5724

1 in → 2 out4.8127 XPM226 B

AYQsmrhm…nAFtUJFn AbKKZbkF…hyn6cwez

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.

1.149 × 10⁹³(94-digit number)

11496998840531811822…36687672152775359999

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

1.149 × 10⁹³(94-digit number)

11496998840531811822…36687672152775359999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.149 × 10⁹³(94-digit number)

11496998840531811822…36687672152775360001

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

2.299 × 10⁹³(94-digit number)

22993997681063623644…73375344305550719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.299 × 10⁹³(94-digit number)

22993997681063623644…73375344305550720001

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

4.598 × 10⁹³(94-digit number)

45987995362127247288…46750688611101439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.598 × 10⁹³(94-digit number)

45987995362127247288…46750688611101440001

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

9.197 × 10⁹³(94-digit number)

91975990724254494576…93501377222202879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.197 × 10⁹³(94-digit number)

91975990724254494576…93501377222202880001

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

1.839 × 10⁹⁴(95-digit number)

18395198144850898915…87002754444405759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.839 × 10⁹⁴(95-digit number)

18395198144850898915…87002754444405760001

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