Block #370,582

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/22/2014, 6:14:40 AM · Difficulty 10.4374 · 6,437,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cb7e24af88b6f02ed0bc50ab6f84d971fbe5145e4e3ae4b396c928635efc5ae

View on Chainz ↗

Height

#370,582

Difficulty

10.437402

Transactions

Size

1.08 KB

Version

Bits

0a6ff98f

Nonce

302,466

Timestamp

1/22/2014, 6:14:40 AM

Confirmations

6,437,552

Mined by

⛏️ P2SHAb64gm8KUnFNR9oWChHpwHnuPjmwRnN1CH

Merkle Root

b7f088811e47bf2a5573dbf3b0e4ff2e2be96b90d5cf493d348a0cf4ab7c686f

Transactions (5)

Coinbase774e9dc9ec2570…15a916e2ffaa80

1 in → 1 out9.2100 XPM109 B

Ab64gm8K…mwRnN1CH

ca4a7d8bf4b169…b0b179c0b339a8

1 in → 2 out8.1362 XPM226 B

AKbRqqVr…6vDQstRb AZTaiuc9…5hQfZCyt

616036c6161b28…fd5efbcbc007c6

1 in → 2 out7.0985 XPM225 B

AbWLT2GX…wtNZrcM3 AYS6GTrA…XAwQrkRk

b32e7f5b81a319…bc93828665f89a

1 in → 2 out7.0054 XPM226 B

AZQ6UPYd…vtKVGM8z AYCpU4J8…8dB4ujDd

c7b01a5e6a0871…e49beca8897eaa

1 in → 2 out7.0766 XPM227 B

AMLrDt5q…wiVmCfvJ Ab3J4ipo…GaHrWuuW

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.

6.094 × 10⁹⁶(97-digit number)

60944896569672906018…56292098730217727999

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

6.094 × 10⁹⁶(97-digit number)

60944896569672906018…56292098730217727999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.094 × 10⁹⁶(97-digit number)

60944896569672906018…56292098730217728001

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

1.218 × 10⁹⁷(98-digit number)

12188979313934581203…12584197460435455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.218 × 10⁹⁷(98-digit number)

12188979313934581203…12584197460435456001

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

2.437 × 10⁹⁷(98-digit number)

24377958627869162407…25168394920870911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.437 × 10⁹⁷(98-digit number)

24377958627869162407…25168394920870912001

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

4.875 × 10⁹⁷(98-digit number)

48755917255738324815…50336789841741823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.875 × 10⁹⁷(98-digit number)

48755917255738324815…50336789841741824001

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

9.751 × 10⁹⁷(98-digit number)

97511834511476649630…00673579683483647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.751 × 10⁹⁷(98-digit number)

97511834511476649630…00673579683483648001

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

Block #370,582

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