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Block #2,127,346

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/21/2017, 10:18:14 PM Β· Difficulty 10.9184 Β· 4,716,572 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f52f84cd51e1aafd286c77bf1ff1742cfc4080b908ff055e64a9d32471671383
View on Chainz β†—

Height

#2,127,346

Difficulty

10.918389

Transactions

1

Size

244 B

Version

2

Bits

0aeb1b90

Nonce

854,427,989

Timestamp

5/21/2017, 10:18:14 PM

Confirmations

4,716,572

Mined by

⛏️ P2SHAMMJ7Ku9ctFmjCbBPtKsnh34K5ZYGbYo5z

Merkle Root

ef328f80061e656cdb8b0b4d569802fbfdfe757fb9df22ab72563fb2af3ec2c3
Transactions (1)
Coinbaseef328f80061e65…563fb2af3ec2c3
1 in β†’ 2 out8.3800 XPM152 B
AMMJ7Ku9…ZYGbYo5zAXbk7f7A…Tx7JECPG
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.

4.494 Γ— 10⁹⁸(99-digit number)
44944154547667453524…82116381326435788799
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
4.494 Γ— 10⁹⁸(99-digit number)
44944154547667453524…82116381326435788799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.494 Γ— 10⁹⁸(99-digit number)
44944154547667453524…82116381326435788801
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
8.988 Γ— 10⁹⁸(99-digit number)
89888309095334907049…64232762652871577599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.988 Γ— 10⁹⁸(99-digit number)
89888309095334907049…64232762652871577601
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
1.797 Γ— 10⁹⁹(100-digit number)
17977661819066981409…28465525305743155199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.797 Γ— 10⁹⁹(100-digit number)
17977661819066981409…28465525305743155201
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
3.595 Γ— 10⁹⁹(100-digit number)
35955323638133962819…56931050611486310399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.595 Γ— 10⁹⁹(100-digit number)
35955323638133962819…56931050611486310401
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
7.191 Γ— 10⁹⁹(100-digit number)
71910647276267925639…13862101222972620799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.191 Γ— 10⁹⁹(100-digit number)
71910647276267925639…13862101222972620801
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:57,995,715 XPMΒ·at block #6,843,917 Β· updates every 60s
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