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Block #50,225

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/16/2013, 12:11:41 AM Β· Difficulty 8.8791 Β· 6,757,735 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a64aac325e117dd1f401ab3576c3633069fff45ed063fc28d611b0f433ea3810
View on Chainz β†—

Height

#50,225

Difficulty

8.879080

Transactions

1

Size

201 B

Version

2

Bits

08e10b69

Nonce

470

Timestamp

7/16/2013, 12:11:41 AM

Confirmations

6,757,735

Mined by

⛏️ P2SHAQz2cBEbtCrbn9CN1FKZZzaLqvc8sJiM3Q

Merkle Root

07ff25f9ca8e350f5c86eaf3ef4e9bb148891fa18e4f1df8e5f43c953144d594
Transactions (1)
Coinbase07ff25f9ca8e35…f43c953144d594
1 in β†’ 1 out12.6700 XPM110 B
AQz2cBEb…c8sJiM3Q
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.284 Γ— 10⁹⁸(99-digit number)
12842145768473960374…44820253833867917279
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.284 Γ— 10⁹⁸(99-digit number)
12842145768473960374…44820253833867917279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.284 Γ— 10⁹⁸(99-digit number)
12842145768473960374…44820253833867917281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.568 Γ— 10⁹⁸(99-digit number)
25684291536947920749…89640507667735834559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.568 Γ— 10⁹⁸(99-digit number)
25684291536947920749…89640507667735834561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
5.136 Γ— 10⁹⁸(99-digit number)
51368583073895841498…79281015335471669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.136 Γ— 10⁹⁸(99-digit number)
51368583073895841498…79281015335471669121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.027 Γ— 10⁹⁹(100-digit number)
10273716614779168299…58562030670943338239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.027 Γ— 10⁹⁹(100-digit number)
10273716614779168299…58562030670943338241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,707,722 XPMΒ·at block #6,807,959 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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