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Block #1,611,495

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/2/2016, 9:30:30 PM Β· Difficulty 10.6057 Β· 5,231,333 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3d0fb6506b8d553f318f893d24d78d3268d1926dc90b6303f442f7fa9922571c
View on Chainz β†—

Height

#1,611,495

Difficulty

10.605680

Transactions

1

Size

199 B

Version

2

Bits

0a9b0de0

Nonce

70,562,280

Timestamp

6/2/2016, 9:30:30 PM

Confirmations

5,231,333

Mined by

⛏️ P2SHAMP4rmHAGQVG8s1BhFcz3nEm9NzE6udEws

Merkle Root

48dddfd95240859943caaeb53e793d4899b43bf8e72646e841a6907ce3b807cc
Transactions (1)
Coinbase48dddfd9524085…a6907ce3b807cc
1 in β†’ 1 out8.8800 XPM109 B
AMP4rmHA…zE6udEws
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.

3.303 Γ— 10⁹⁴(95-digit number)
33035497792035016213…24356363240711331839
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
3.303 Γ— 10⁹⁴(95-digit number)
33035497792035016213…24356363240711331839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.303 Γ— 10⁹⁴(95-digit number)
33035497792035016213…24356363240711331841
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
6.607 Γ— 10⁹⁴(95-digit number)
66070995584070032426…48712726481422663679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.607 Γ— 10⁹⁴(95-digit number)
66070995584070032426…48712726481422663681
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
1.321 Γ— 10⁹⁡(96-digit number)
13214199116814006485…97425452962845327359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.321 Γ— 10⁹⁡(96-digit number)
13214199116814006485…97425452962845327361
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
2.642 Γ— 10⁹⁡(96-digit number)
26428398233628012970…94850905925690654719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.642 Γ— 10⁹⁡(96-digit number)
26428398233628012970…94850905925690654721
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
5.285 Γ— 10⁹⁡(96-digit number)
52856796467256025941…89701811851381309439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.285 Γ— 10⁹⁡(96-digit number)
52856796467256025941…89701811851381309441
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:57,986,967 XPMΒ·at block #6,842,827 Β· updates every 60s
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