Block #707,925

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/5/2014, 7:03:03 AM · Difficulty 10.9580 · 6,088,024 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52fc3ac18bf53e6ed8b0da50adcc04eb87a1c87e6c68a677c9b03284b71e755b

View on Chainz ↗

Height

#707,925

Difficulty

10.957977

Transactions

Size

734 B

Version

Bits

0af53e00

Nonce

27,281

Timestamp

9/5/2014, 7:03:03 AM

Confirmations

6,088,024

Mined by

⛏️ UAdnG9gQ7MrBtC7Bjg1kQZzjdPFN9B7mA2p

Merkle Root

4334ca4e9f345b66a9790f7f533c2083f1860cf4b3153dfffeba99ff8ba72afc

Transactions (1)

Coinbase4334ca4e9f345b…ba99ff8ba72afc

1 in → 17 out8.3100 XPM641 B

AdnG9gQ7…N9B7mA2p AJzWx2VD…j4ZSMit5 APfZjrNu…Wvzt6AFp AebWhrRm…K61Qrkws AJCeFGQe…Ab2py48B

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.

3.851 × 10¹⁰¹(102-digit number)

38513580428863531399…68324388177910319359

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

3.851 × 10¹⁰¹(102-digit number)

38513580428863531399…68324388177910319359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.851 × 10¹⁰¹(102-digit number)

38513580428863531399…68324388177910319361

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

7.702 × 10¹⁰¹(102-digit number)

77027160857727062798…36648776355820638719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.702 × 10¹⁰¹(102-digit number)

77027160857727062798…36648776355820638721

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

1.540 × 10¹⁰²(103-digit number)

15405432171545412559…73297552711641277439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.540 × 10¹⁰²(103-digit number)

15405432171545412559…73297552711641277441

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

3.081 × 10¹⁰²(103-digit number)

30810864343090825119…46595105423282554879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.081 × 10¹⁰²(103-digit number)

30810864343090825119…46595105423282554881

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

6.162 × 10¹⁰²(103-digit number)

61621728686181650239…93190210846565109759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.162 × 10¹⁰²(103-digit number)

61621728686181650239…93190210846565109761

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.232 × 10¹⁰³(104-digit number)

12324345737236330047…86380421693130219519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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