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Block #2,077,809

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/19/2017, 2:01:46 PM Β· Difficulty 10.8510 Β· 4,762,322 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39f2cc1de43cf6f4045a271150e77e97076bf6caaf966b47f32648df958e6310
View on Chainz β†—

Height

#2,077,809

Difficulty

10.851034

Transactions

1

Size

200 B

Version

2

Bits

0ad9dd61

Nonce

541,214,469

Timestamp

4/19/2017, 2:01:46 PM

Confirmations

4,762,322

Mined by

⛏️ P2SHALBC8q1a6LM57mXNHYaYm7C4mnyytCMsho

Merkle Root

1fbf694aaa6d92e7f07a5c992cc751643df1bb47bad1b4bada17eb559f45d7a2
Transactions (1)
Coinbase1fbf694aaa6d92…17eb559f45d7a2
1 in β†’ 1 out8.4800 XPM110 B
ALBC8q1a…yytCMsho
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.

1.633 Γ— 10⁹⁴(95-digit number)
16336696877531728640…55306606760763006719
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
1.633 Γ— 10⁹⁴(95-digit number)
16336696877531728640…55306606760763006719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.633 Γ— 10⁹⁴(95-digit number)
16336696877531728640…55306606760763006721
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
3.267 Γ— 10⁹⁴(95-digit number)
32673393755063457281…10613213521526013439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.267 Γ— 10⁹⁴(95-digit number)
32673393755063457281…10613213521526013441
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
6.534 Γ— 10⁹⁴(95-digit number)
65346787510126914562…21226427043052026879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.534 Γ— 10⁹⁴(95-digit number)
65346787510126914562…21226427043052026881
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
1.306 Γ— 10⁹⁡(96-digit number)
13069357502025382912…42452854086104053759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.306 Γ— 10⁹⁡(96-digit number)
13069357502025382912…42452854086104053761
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
2.613 Γ— 10⁹⁡(96-digit number)
26138715004050765825…84905708172208107519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.613 Γ— 10⁹⁡(96-digit number)
26138715004050765825…84905708172208107521
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:57,965,362 XPMΒ·at block #6,840,130 Β· updates every 60s
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