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Block #883,619

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2015, 9:47:31 PM Β· Difficulty 10.9591 Β· 5,912,829 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
38ed1e60b500a607c6203b9d58fadc70dadc705064568d6fd4e15dd0e4b52596
View on Chainz β†—

Height

#883,619

Difficulty

10.959136

Transactions

2

Size

723 B

Version

2

Bits

0af589ef

Nonce

864,819,975

Timestamp

1/5/2015, 9:47:31 PM

Confirmations

5,912,829

Mined by

⛏️ P2SHAGVcZni27hciDVreBYSNHsjt9doBFk4veW

Merkle Root

e8fa1bdd3215f2531a7b0e3cdfc2260c03ac3d45715ad049dc1e1b765990df8f
Transactions (2)
Coinbasee23b514f785fee…5766b8811d5925
1 in β†’ 1 out8.3200 XPM109 B
AGVcZni2…oBFk4veW
219faee4d6868e…e4648f65854f5e
3 in β†’ 2 out160.9100 XPM524 B
AZvzB4xZ…FVnNM1nPAbfEn7Nt…55CdqUCR
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.

8.043 Γ— 10⁹³(94-digit number)
80430305633312387308…52093129192192057279
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
8.043 Γ— 10⁹³(94-digit number)
80430305633312387308…52093129192192057279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.043 Γ— 10⁹³(94-digit number)
80430305633312387308…52093129192192057281
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
1.608 Γ— 10⁹⁴(95-digit number)
16086061126662477461…04186258384384114559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.608 Γ— 10⁹⁴(95-digit number)
16086061126662477461…04186258384384114561
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
3.217 Γ— 10⁹⁴(95-digit number)
32172122253324954923…08372516768768229119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.217 Γ— 10⁹⁴(95-digit number)
32172122253324954923…08372516768768229121
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
6.434 Γ— 10⁹⁴(95-digit number)
64344244506649909846…16745033537536458239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.434 Γ— 10⁹⁴(95-digit number)
64344244506649909846…16745033537536458241
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
1.286 Γ— 10⁹⁡(96-digit number)
12868848901329981969…33490067075072916479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.286 Γ— 10⁹⁡(96-digit number)
12868848901329981969…33490067075072916481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
2.573 Γ— 10⁹⁡(96-digit number)
25737697802659963938…66980134150145832959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,615,578 XPMΒ·at block #6,796,447 Β· updates every 60s
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