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Block #470,771

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/2/2014, 3:57:38 AM Β· Difficulty 10.4287 Β· 6,340,112 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d394b8eafa574855db419e82df8c06f5f54cacd8564458c724c6e5b847f481a
View on Chainz β†—

Height

#470,771

Difficulty

10.428671

Transactions

1

Size

207 B

Version

2

Bits

0a6dbd62

Nonce

104,704

Timestamp

4/2/2014, 3:57:38 AM

Confirmations

6,340,112

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7d38aac5bc0f8bbec3e701da00e7aea8b5a7e504c7ec93ee1633b4398cf5b4db
Transactions (1)
Coinbase7d38aac5bc0f8b…33b4398cf5b4db
1 in β†’ 1 out9.1800 XPM116 B
AbwWkWZt…kawDhufa
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.

5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480919
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
5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.592 Γ— 10⁹⁷(98-digit number)
55929342948817183747…82082871128537480921
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
1.118 Γ— 10⁹⁸(99-digit number)
11185868589763436749…64165742257074961839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.118 Γ— 10⁹⁸(99-digit number)
11185868589763436749…64165742257074961841
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
2.237 Γ— 10⁹⁸(99-digit number)
22371737179526873499…28331484514149923679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.237 Γ— 10⁹⁸(99-digit number)
22371737179526873499…28331484514149923681
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
4.474 Γ— 10⁹⁸(99-digit number)
44743474359053746998…56662969028299847359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.474 Γ— 10⁹⁸(99-digit number)
44743474359053746998…56662969028299847361
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
8.948 Γ— 10⁹⁸(99-digit number)
89486948718107493996…13325938056599694719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.948 Γ— 10⁹⁸(99-digit number)
89486948718107493996…13325938056599694721
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:57,731,164 XPMΒ·at block #6,810,882 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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