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Block #363,967

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/17/2014, 6:25:25 PM Β· Difficulty 10.4183 Β· 6,463,142 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5abb77f716d70086a33cf8a793321af092098d590a966cf501f15111594ec74e
View on Chainz β†—

Height

#363,967

Difficulty

10.418330

Transactions

1

Size

212 B

Version

2

Bits

0a6b17b0

Nonce

1,036,230

Timestamp

1/17/2014, 6:25:25 PM

Confirmations

6,463,142

Mined by

⛏️ P2SHAPS8BXgGGKDMhmeQhGa5yYZR2HvuDwPaoc

Merkle Root

e092f793e2750acde1d81bd5423a589c22fd9265c87a90432ade3893a7679ff0
Transactions (1)
Coinbasee092f793e2750a…de3893a7679ff0
1 in β†’ 1 out9.2000 XPM118 B
APS8BXgG…vuDwPaoc
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.

3.906 Γ— 10¹⁰⁴(105-digit number)
39064806244466088989…01726886225651957759
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
3.906 Γ— 10¹⁰⁴(105-digit number)
39064806244466088989…01726886225651957759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.906 Γ— 10¹⁰⁴(105-digit number)
39064806244466088989…01726886225651957761
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
7.812 Γ— 10¹⁰⁴(105-digit number)
78129612488932177979…03453772451303915519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.812 Γ— 10¹⁰⁴(105-digit number)
78129612488932177979…03453772451303915521
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
1.562 Γ— 10¹⁰⁡(106-digit number)
15625922497786435595…06907544902607831039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.562 Γ— 10¹⁰⁡(106-digit number)
15625922497786435595…06907544902607831041
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
3.125 Γ— 10¹⁰⁡(106-digit number)
31251844995572871191…13815089805215662079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.125 Γ— 10¹⁰⁡(106-digit number)
31251844995572871191…13815089805215662081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
6.250 Γ— 10¹⁰⁡(106-digit number)
62503689991145742383…27630179610431324159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.250 Γ— 10¹⁰⁡(106-digit number)
62503689991145742383…27630179610431324161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 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
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 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:57,861,051 XPMΒ·at block #6,827,108 Β· updates every 60s
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