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Block #1,041,473

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2015, 9:06:41 AM Β· Difficulty 10.7253 Β· 5,791,677 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
33e815d812b67581a6527b72364ccbbfd8452b9c30e35c5143c2ba2997088db6
View on Chainz β†—

Height

#1,041,473

Difficulty

10.725317

Transactions

1

Size

243 B

Version

2

Bits

0ab9ae61

Nonce

457,286,398

Timestamp

5/2/2015, 9:06:41 AM

Confirmations

5,791,677

Mined by

⛏️ P2SHAUV3ZXsawxZuaXubcanNHw2sUMP3xQCbyH

Merkle Root

d17a7f451129c0a367fb98e120daf1474fa368b34319780e4996414d9402ac75
Transactions (1)
Coinbased17a7f451129c0…96414d9402ac75
1 in β†’ 2 out8.6800 XPM152 B
AUV3ZXsa…P3xQCbyHALPu3s2c…EJXLjVFh
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.

1.874 Γ— 10⁹⁷(98-digit number)
18742111834021269439…91413167274704404479
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
1.874 Γ— 10⁹⁷(98-digit number)
18742111834021269439…91413167274704404479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.874 Γ— 10⁹⁷(98-digit number)
18742111834021269439…91413167274704404481
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
3.748 Γ— 10⁹⁷(98-digit number)
37484223668042538878…82826334549408808959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.748 Γ— 10⁹⁷(98-digit number)
37484223668042538878…82826334549408808961
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
7.496 Γ— 10⁹⁷(98-digit number)
74968447336085077757…65652669098817617919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.496 Γ— 10⁹⁷(98-digit number)
74968447336085077757…65652669098817617921
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
1.499 Γ— 10⁹⁸(99-digit number)
14993689467217015551…31305338197635235839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.499 Γ— 10⁹⁸(99-digit number)
14993689467217015551…31305338197635235841
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
2.998 Γ— 10⁹⁸(99-digit number)
29987378934434031102…62610676395270471679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.998 Γ— 10⁹⁸(99-digit number)
29987378934434031102…62610676395270471681
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:57,909,377 XPMΒ·at block #6,833,149 Β· updates every 60s
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