Block #373,440

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 7:46:31 AM · Difficulty 10.4252 · 6,432,250 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5810eedff6574177ceab2c4f2eda28b49c3781395bd23fb0d901dee11ca886a6

View on Chainz ↗

Height

#373,440

Difficulty

10.425188

Transactions

Size

1.26 KB

Version

Bits

0a6cd91a

Nonce

823,644

Timestamp

1/24/2014, 7:46:31 AM

Confirmations

6,432,250

Mined by

⛏️ P2SHAZwEWFtt1zVMgZRPshpC9tMd3DMi6kRxp5

Merkle Root

7d0c830412ca15e649825f4a0036bedf2faf43bc17d16fffa3ad596cd7d9350a

Transactions (2)

Coinbase3eb572d1d65a7b…dc3c928910d532

1 in → 1 out9.2100 XPM109 B

AZwEWFtt…Mi6kRxp5

ffcd3552c7741e…49f90a0c87f13a

5 in → 15 out45.8340 XPM1.06 KB

AeKNrjNj…1NEq95Ta AKXVCBXq…X8vh766Q ATg39xTo…L817ySF3 AdYH33yX…NKufJznD AZ1Zr8Tc…rVFtzx4a

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.

1.107 × 10¹⁰⁰(101-digit number)

11070022957028287016…67789504997818413759

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

1.107 × 10¹⁰⁰(101-digit number)

11070022957028287016…67789504997818413759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10¹⁰⁰(101-digit number)

11070022957028287016…67789504997818413761

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

2.214 × 10¹⁰⁰(101-digit number)

22140045914056574033…35579009995636827519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.214 × 10¹⁰⁰(101-digit number)

22140045914056574033…35579009995636827521

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

4.428 × 10¹⁰⁰(101-digit number)

44280091828113148066…71158019991273655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.428 × 10¹⁰⁰(101-digit number)

44280091828113148066…71158019991273655041

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

8.856 × 10¹⁰⁰(101-digit number)

88560183656226296132…42316039982547310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.856 × 10¹⁰⁰(101-digit number)

88560183656226296132…42316039982547310081

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

1.771 × 10¹⁰¹(102-digit number)

17712036731245259226…84632079965094620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.771 × 10¹⁰¹(102-digit number)

17712036731245259226…84632079965094620161

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