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Block #428,806

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2014, 8:59:53 AM Β· Difficulty 10.3421 Β· 6,387,627 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
580f8821de7f963dd4dfd91cbd6a31ecb1f8595bd3184c9f24bdcb20ecc93c65
View on Chainz β†—

Height

#428,806

Difficulty

10.342083

Transactions

1

Size

220 B

Version

2

Bits

0a5792c2

Nonce

80,040

Timestamp

3/4/2014, 8:59:53 AM

Confirmations

6,387,627

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

41f007e787509aba68d4157c5393538dd69ebf893761c21dcd1594ccf893d2a8
Transactions (1)
Coinbase41f007e787509a…1594ccf893d2a8
1 in β†’ 2 out9.3400 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

1.624 Γ— 10⁹³(94-digit number)
16247733329183524131…22114704101583008369
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
1.624 Γ— 10⁹³(94-digit number)
16247733329183524131…22114704101583008369
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.624 Γ— 10⁹³(94-digit number)
16247733329183524131…22114704101583008371
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
3.249 Γ— 10⁹³(94-digit number)
32495466658367048263…44229408203166016739
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.249 Γ— 10⁹³(94-digit number)
32495466658367048263…44229408203166016741
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
6.499 Γ— 10⁹³(94-digit number)
64990933316734096527…88458816406332033479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.499 Γ— 10⁹³(94-digit number)
64990933316734096527…88458816406332033481
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
1.299 Γ— 10⁹⁴(95-digit number)
12998186663346819305…76917632812664066959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.299 Γ— 10⁹⁴(95-digit number)
12998186663346819305…76917632812664066961
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
2.599 Γ— 10⁹⁴(95-digit number)
25996373326693638611…53835265625328133919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.599 Γ— 10⁹⁴(95-digit number)
25996373326693638611…53835265625328133921
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:57,775,591 XPMΒ·at block #6,816,432 Β· updates every 60s
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