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Block #1,868,417

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2016, 5:25:45 PM Β· Difficulty 10.6787 Β· 4,946,705 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3cd5ac5b86d3135f82b2f0c3d19521d8c00508f49b143247e042f7d9dc7fcb24
View on Chainz β†—

Height

#1,868,417

Difficulty

10.678686

Transactions

2

Size

1020 B

Version

2

Bits

0aadbe5d

Nonce

182,779,454

Timestamp

11/27/2016, 5:25:45 PM

Confirmations

4,946,705

Mined by

⛏️ P2SHAZZNXFcfnUvJUBisfxwpPAsgMbRMBdNX8y

Merkle Root

e45d02db30d620b571e2cd33c8d8a5d023f02c3efbc9634219efc80de46e437e
Transactions (2)
Coinbased143880f2ab119…030d3fbed75ae5
1 in β†’ 1 out8.7700 XPM110 B
AZZNXFcf…RMBdNX8y
12ed31140615e3…f885d00d7d8dee
5 in β†’ 2 out311.9050 XPM820 B
ASMMZz4E…7FeHYYcpAHyt5CEx…gH88XzWn
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.

2.203 Γ— 10⁹⁴(95-digit number)
22030290153464066913…06641366975350558239
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
2.203 Γ— 10⁹⁴(95-digit number)
22030290153464066913…06641366975350558239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.203 Γ— 10⁹⁴(95-digit number)
22030290153464066913…06641366975350558241
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
4.406 Γ— 10⁹⁴(95-digit number)
44060580306928133827…13282733950701116479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.406 Γ— 10⁹⁴(95-digit number)
44060580306928133827…13282733950701116481
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
8.812 Γ— 10⁹⁴(95-digit number)
88121160613856267654…26565467901402232959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.812 Γ— 10⁹⁴(95-digit number)
88121160613856267654…26565467901402232961
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
1.762 Γ— 10⁹⁡(96-digit number)
17624232122771253530…53130935802804465919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.762 Γ— 10⁹⁡(96-digit number)
17624232122771253530…53130935802804465921
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
3.524 Γ— 10⁹⁡(96-digit number)
35248464245542507061…06261871605608931839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.524 Γ— 10⁹⁡(96-digit number)
35248464245542507061…06261871605608931841
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:57,765,069 XPMΒ·at block #6,815,121 Β· updates every 60s
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