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Block #2,187,866

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/1/2017, 11:24:42 AM Β· Difficulty 10.9477 Β· 4,648,804 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1843de9c37f07712f5614fbdf86121000fa5faa35afd9ec5fb39de51dc7a0016
View on Chainz β†—

Height

#2,187,866

Difficulty

10.947662

Transactions

2

Size

871 B

Version

2

Bits

0af29a02

Nonce

124,054,698

Timestamp

7/1/2017, 11:24:42 AM

Confirmations

4,648,804

Mined by

⛏️ P2SHAT9r95mHTCU68dxp41EVu8GaWykepxXe5p

Merkle Root

ccc6eea549e45fd6737e1a2319a60085aad77a76209eeb5206911368ac880065
Transactions (2)
Coinbasecaeaacbb18e359…ddb51657118fbd
1 in β†’ 1 out8.3400 XPM110 B
AT9r95mH…kepxXe5p
d676545faeee28…8719a771167a74
4 in β†’ 2 out914.5002 XPM671 B
AXd645dq…zw4HK9fcANjAdo5o…SxMHuzym
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.

1.138 Γ— 10⁹⁡(96-digit number)
11383911446188774871…54564973172473603199
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
1.138 Γ— 10⁹⁡(96-digit number)
11383911446188774871…54564973172473603199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.138 Γ— 10⁹⁡(96-digit number)
11383911446188774871…54564973172473603201
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
2.276 Γ— 10⁹⁡(96-digit number)
22767822892377549742…09129946344947206399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.276 Γ— 10⁹⁡(96-digit number)
22767822892377549742…09129946344947206401
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
4.553 Γ— 10⁹⁡(96-digit number)
45535645784755099485…18259892689894412799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.553 Γ— 10⁹⁡(96-digit number)
45535645784755099485…18259892689894412801
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
9.107 Γ— 10⁹⁡(96-digit number)
91071291569510198970…36519785379788825599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.107 Γ— 10⁹⁡(96-digit number)
91071291569510198970…36519785379788825601
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
1.821 Γ— 10⁹⁢(97-digit number)
18214258313902039794…73039570759577651199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.821 Γ— 10⁹⁢(97-digit number)
18214258313902039794…73039570759577651201
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:57,937,638 XPMΒ·at block #6,836,669 Β· updates every 60s
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