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Block #901,820

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2015, 9:12:28 PM Β· Difficulty 10.9408 Β· 5,907,519 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3182b323a19befa7fd2f9775580fef06be9e9092b9d1296e0ff883e7f85c946f
View on Chainz β†—

Height

#901,820

Difficulty

10.940826

Transactions

2

Size

2.34 KB

Version

2

Bits

0af0d9fa

Nonce

87,967,282

Timestamp

1/19/2015, 9:12:28 PM

Confirmations

5,907,519

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

80cbdafefd17cbed2ce8584501ef8f21135c9cc654c4298d5a91ccdf1a72aabb
Transactions (2)
Coinbase18465a50af39b1…26f502b79ab07f
1 in β†’ 1 out8.3700 XPM116 B
ANSXnLY2…Sd25TjkD
965f1a59ee204b…f4581ebec7182b
14 in β†’ 3 out3637.0774 XPM2.14 KB
AQUC7Hue…LL2XMoNYAQ5fy2sY…PEW6voxhAYUhiCz3…yGae52dr
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.

2.600 Γ— 10⁹⁡(96-digit number)
26009118739999759992…08394610239275396479
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
2.600 Γ— 10⁹⁡(96-digit number)
26009118739999759992…08394610239275396479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.600 Γ— 10⁹⁡(96-digit number)
26009118739999759992…08394610239275396481
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
5.201 Γ— 10⁹⁡(96-digit number)
52018237479999519985…16789220478550792959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.201 Γ— 10⁹⁡(96-digit number)
52018237479999519985…16789220478550792961
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
1.040 Γ— 10⁹⁢(97-digit number)
10403647495999903997…33578440957101585919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.040 Γ— 10⁹⁢(97-digit number)
10403647495999903997…33578440957101585921
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
2.080 Γ— 10⁹⁢(97-digit number)
20807294991999807994…67156881914203171839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.080 Γ— 10⁹⁢(97-digit number)
20807294991999807994…67156881914203171841
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
4.161 Γ— 10⁹⁢(97-digit number)
41614589983999615988…34313763828406343679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.161 Γ— 10⁹⁢(97-digit number)
41614589983999615988…34313763828406343681
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:57,718,777 XPMΒ·at block #6,809,338 Β· updates every 60s
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