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Block #217,231

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/19/2013, 5:39:49 AM Β· Difficulty 9.9277 Β· 6,577,705 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a01d9ee0a74a7e7b52e3e400c780f01f887455773f0c72b9316e53bcb06d78cb
View on Chainz β†—

Height

#217,231

Difficulty

9.927725

Transactions

1

Size

198 B

Version

2

Bits

09ed7f62

Nonce

14,533

Timestamp

10/19/2013, 5:39:49 AM

Confirmations

6,577,705

Mined by

⛏️ P2SHAS6zmvkv48fxzAQajjxPeSjfs44CVw3yd9

Merkle Root

e12dfaad45631b05c59186ec58b84d94c3eed0066ed8fd1233379067d907a34e
Transactions (1)
Coinbasee12dfaad45631b…379067d907a34e
1 in β†’ 1 out10.1300 XPM109 B
AS6zmvkv…4CVw3yd9
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.

5.427 Γ— 10⁹²(93-digit number)
54273068051121631676…90865338318936883199
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
5.427 Γ— 10⁹²(93-digit number)
54273068051121631676…90865338318936883199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.427 Γ— 10⁹²(93-digit number)
54273068051121631676…90865338318936883201
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
1.085 Γ— 10⁹³(94-digit number)
10854613610224326335…81730676637873766399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.085 Γ— 10⁹³(94-digit number)
10854613610224326335…81730676637873766401
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
2.170 Γ— 10⁹³(94-digit number)
21709227220448652670…63461353275747532799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.170 Γ— 10⁹³(94-digit number)
21709227220448652670…63461353275747532801
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
4.341 Γ— 10⁹³(94-digit number)
43418454440897305341…26922706551495065599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.341 Γ— 10⁹³(94-digit number)
43418454440897305341…26922706551495065601
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
8.683 Γ— 10⁹³(94-digit number)
86836908881794610682…53845413102990131199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9

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:57,603,522 XPMΒ·at block #6,794,935 Β· updates every 60s
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