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Block #1,762,782

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2016, 2:10:26 PM Β· Difficulty 10.7382 Β· 5,046,977 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ccea2929e330356cbb2acee07f6b8e68b13e678a4ea1db000fa8b2a8dc161c63
View on Chainz β†—

Height

#1,762,782

Difficulty

10.738225

Transactions

2

Size

688 B

Version

2

Bits

0abcfc4e

Nonce

1,715,334,350

Timestamp

9/14/2016, 2:10:26 PM

Confirmations

5,046,977

Mined by

⛏️ P2SHAbi2PFMfFD2e8ZzgVUR7zqVGMUs4RAPukF

Merkle Root

ebe368647488a7db610cb0bd1d4afab76ebae0821c1feb831679d12fcf70635a
Transactions (2)
Coinbasec0e22a6ec7bcfa…b58296191cad42
1 in β†’ 1 out8.6700 XPM109 B
Abi2PFMf…s4RAPukF
c9c5b465517da5…e488546ece26ec
3 in β†’ 1 out20000.0000 XPM489 B
AYKArr5V…V9VqiqCZ
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.

8.237 Γ— 10⁹⁡(96-digit number)
82379938617930926223…58708610127700469759
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
8.237 Γ— 10⁹⁡(96-digit number)
82379938617930926223…58708610127700469759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.237 Γ— 10⁹⁡(96-digit number)
82379938617930926223…58708610127700469761
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
1.647 Γ— 10⁹⁢(97-digit number)
16475987723586185244…17417220255400939519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.647 Γ— 10⁹⁢(97-digit number)
16475987723586185244…17417220255400939521
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
3.295 Γ— 10⁹⁢(97-digit number)
32951975447172370489…34834440510801879039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.295 Γ— 10⁹⁢(97-digit number)
32951975447172370489…34834440510801879041
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
6.590 Γ— 10⁹⁢(97-digit number)
65903950894344740978…69668881021603758079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.590 Γ— 10⁹⁢(97-digit number)
65903950894344740978…69668881021603758081
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
1.318 Γ— 10⁹⁷(98-digit number)
13180790178868948195…39337762043207516159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.318 Γ— 10⁹⁷(98-digit number)
13180790178868948195…39337762043207516161
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:57,722,158 XPMΒ·at block #6,809,758 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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