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Block #309,861

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 7:18:13 PM Β· Difficulty 9.9950 Β· 6,517,301 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7aa0b556164c930f0204ffd2981d5d271dbca423c5f52d43f7137d100ebdae7c
View on Chainz β†—

Height

#309,861

Difficulty

9.994989

Transactions

1

Size

210 B

Version

2

Bits

09feb794

Nonce

67,108,956

Timestamp

12/13/2013, 7:18:13 PM

Confirmations

6,517,301

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

df07472c9be3296cf481b017007e8e4fadc1f3f93db646c37169047566c54921
Transactions (1)
Coinbasedf07472c9be329…69047566c54921
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

1.522 Γ— 10¹⁰⁴(105-digit number)
15222575186097889986…16319056530994295939
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
1.522 Γ— 10¹⁰⁴(105-digit number)
15222575186097889986…16319056530994295939
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.522 Γ— 10¹⁰⁴(105-digit number)
15222575186097889986…16319056530994295941
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
3.044 Γ— 10¹⁰⁴(105-digit number)
30445150372195779973…32638113061988591879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.044 Γ— 10¹⁰⁴(105-digit number)
30445150372195779973…32638113061988591881
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
6.089 Γ— 10¹⁰⁴(105-digit number)
60890300744391559946…65276226123977183759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.089 Γ— 10¹⁰⁴(105-digit number)
60890300744391559946…65276226123977183761
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
1.217 Γ— 10¹⁰⁡(106-digit number)
12178060148878311989…30552452247954367519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.217 Γ— 10¹⁰⁡(106-digit number)
12178060148878311989…30552452247954367521
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
2.435 Γ— 10¹⁰⁡(106-digit number)
24356120297756623978…61104904495908735039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.435 Γ— 10¹⁰⁡(106-digit number)
24356120297756623978…61104904495908735041
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:57,861,481 XPMΒ·at block #6,827,161 Β· updates every 60s
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