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Block #648,883

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2014, 3:14:09 PM Β· Difficulty 10.9515 Β· 6,160,609 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1752d3c826862ab17d227eee33375a7434bfdf5e6be906c547e8ee28e840dedc
View on Chainz β†—

Height

#648,883

Difficulty

10.951450

Transactions

2

Size

3.72 KB

Version

2

Bits

0af39242

Nonce

108,884,277

Timestamp

7/26/2014, 3:14:09 PM

Confirmations

6,160,609

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f46098d7dbca757d60b9c4b859c097e821dacabc139293066eaad4631958608c
Transactions (2)
Coinbase5894db89613c9b…83fb5a850dd8ba
1 in β†’ 1 out8.3600 XPM116 B
ANSXnLY2…Sd25TjkD
e9fda06d07cee1…69a04fa8437e11
24 in β†’ 1 out356.5328 XPM3.52 KB
AHSYuthm…8ZKze41E
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.

3.325 Γ— 10⁹⁷(98-digit number)
33254016624957461391…66870429986621735679
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
3.325 Γ— 10⁹⁷(98-digit number)
33254016624957461391…66870429986621735679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.325 Γ— 10⁹⁷(98-digit number)
33254016624957461391…66870429986621735681
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
6.650 Γ— 10⁹⁷(98-digit number)
66508033249914922783…33740859973243471359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.650 Γ— 10⁹⁷(98-digit number)
66508033249914922783…33740859973243471361
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
1.330 Γ— 10⁹⁸(99-digit number)
13301606649982984556…67481719946486942719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.330 Γ— 10⁹⁸(99-digit number)
13301606649982984556…67481719946486942721
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
2.660 Γ— 10⁹⁸(99-digit number)
26603213299965969113…34963439892973885439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.660 Γ— 10⁹⁸(99-digit number)
26603213299965969113…34963439892973885441
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
5.320 Γ— 10⁹⁸(99-digit number)
53206426599931938227…69926879785947770879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.320 Γ— 10⁹⁸(99-digit number)
53206426599931938227…69926879785947770881
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:57,720,009 XPMΒ·at block #6,809,491 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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