Block #616,029

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/4/2014, 8:00:25 AM · Difficulty 10.9423 · 6,178,819 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01e395e9d15fb1c94d0f4b9e0ea7504514571bfb7f3e5eb52b1f95d6968804a0

View on Chainz ↗

Height

#616,029

Difficulty

10.942335

Transactions

Size

1.22 KB

Version

Bits

0af13ce2

Nonce

250,889,544

Timestamp

7/4/2014, 8:00:25 AM

Confirmations

6,178,819

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5feb602fca404c8bde45f12a554e4a84f0d1b441704cd1f1c07812a4e4706eff

Transactions (3)

Coinbase9869a192f65d70…190dc261f9e6e7

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

d2002475730a14…5734720ea3b7c1

5 in → 2 out36.7886 XPM816 B

AeEiNRtN…cFE1Znew AJofcPVi…KaTgbzFV

2714ca56dfa875…6de6ace588aa74

1 in → 2 out5.1223 XPM227 B

AJzsvAcf…dGXGcHcY AJPSj4aY…V9S9Bt73

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.

1.475 × 10¹⁰⁰(101-digit number)

14756403640248154131…34692520222665564159

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

1.475 × 10¹⁰⁰(101-digit number)

14756403640248154131…34692520222665564159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.475 × 10¹⁰⁰(101-digit number)

14756403640248154131…34692520222665564161

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

2.951 × 10¹⁰⁰(101-digit number)

29512807280496308263…69385040445331128319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.951 × 10¹⁰⁰(101-digit number)

29512807280496308263…69385040445331128321

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

5.902 × 10¹⁰⁰(101-digit number)

59025614560992616526…38770080890662256639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.902 × 10¹⁰⁰(101-digit number)

59025614560992616526…38770080890662256641

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

1.180 × 10¹⁰¹(102-digit number)

11805122912198523305…77540161781324513279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.180 × 10¹⁰¹(102-digit number)

11805122912198523305…77540161781324513281

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

2.361 × 10¹⁰¹(102-digit number)

23610245824397046610…55080323562649026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.361 × 10¹⁰¹(102-digit number)

23610245824397046610…55080323562649026561

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

4.722 × 10¹⁰¹(102-digit number)

47220491648794093221…10160647125298053119

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