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Block #692,620

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/25/2014, 6:56:17 PM Β· Difficulty 10.9559 Β· 6,106,317 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25b11a29853e2a404dd6a28e4c61a6b87df546dfa50987afad7b61ea0ea9697d
View on Chainz β†—

Height

#692,620

Difficulty

10.955890

Transactions

2

Size

877 B

Version

2

Bits

0af4b53c

Nonce

523,944,419

Timestamp

8/25/2014, 6:56:17 PM

Confirmations

6,106,317

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2b75150c3ea674b14387e989f815e1fea8f8c5a5310c67ade8aea3fc5a72851e
Transactions (2)
Coinbasea662c8634bfd6b…02b3fcc9cbfb3c
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
c117d6210508fd…2a79e653762e46
4 in β†’ 2 out23.7877 XPM670 B
AVp7b9ZK…5SAcL2PpAToJbUTu…9KMMxzWB
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.

3.944 Γ— 10⁹⁢(97-digit number)
39444080372399313779…49323119848164188159
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
3.944 Γ— 10⁹⁢(97-digit number)
39444080372399313779…49323119848164188159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.944 Γ— 10⁹⁢(97-digit number)
39444080372399313779…49323119848164188161
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
7.888 Γ— 10⁹⁢(97-digit number)
78888160744798627559…98646239696328376319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.888 Γ— 10⁹⁢(97-digit number)
78888160744798627559…98646239696328376321
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
1.577 Γ— 10⁹⁷(98-digit number)
15777632148959725511…97292479392656752639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.577 Γ— 10⁹⁷(98-digit number)
15777632148959725511…97292479392656752641
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
3.155 Γ— 10⁹⁷(98-digit number)
31555264297919451023…94584958785313505279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.155 Γ— 10⁹⁷(98-digit number)
31555264297919451023…94584958785313505281
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
6.311 Γ— 10⁹⁷(98-digit number)
63110528595838902047…89169917570627010559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.311 Γ— 10⁹⁷(98-digit number)
63110528595838902047…89169917570627010561
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:57,635,531 XPMΒ·at block #6,798,936 Β· updates every 60s
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